Reference is hereby made to provisional patent application Ser. No. 60/004,253 filed Sep. 25, 1995, the benefit of the filing date of which is claimed herein.
1. Field of the Invention
The present invention relates to a kinematic structure for spatial positioning devices and, more particularly, to a hexahedron coordinate measuring machine (CMM), a method of initializing same and an improved universal joint for use in connection with coordinate measuring machines.
2. State of the Art
The present invention concerns the application of a novel parallel kinematic system to coordinate measuring machines. Coordinate measuring machines (CMMs) are widely used in industry for dimensional inspection of manufactured parts. CMMs normally consist of several functional components. A table is provided where the parts to be measured can be fixtured. A probe senses the edges and surfaces of the features to be measured on the part. A kinematic structure provides relative motion between the part and the probe and allows the probe to be moved to the proper locations on the part. A position sensing system reports the spatial coordinates of the probe at each measured location. These coordinate locations are processed by measurement software to determine the locations, dimensions and geometry of the part features.
The vast majority of CMMs use a kinematic structure consisting of a serial chain of three prismatic joints arranged to be mutually perpendicular, thus providing a physical embodiment of a Cartesian coordinate system. The position sensing system is then provided by displacement sensors (scales) along each slide (coordinate axis). A variety of probes may be carried by these machines, including touch-trigger, capacitance and optical devices. Since this kinematic structure does not allow the probe to be oriented with respect to the workpiece, some probe manufacturers provide motorized or manual indexing capability. This allows the probe to be oriented as needed with respect to particular features on the part.
The measurement accuracy of these types of CMMs is greatly affected by the precision with which the individual components are manufactured and assembled. Individual axis slides will not be perfectly straight or orthogonal to the others. Elastic deformations of the structural components compound this problem. For this reason, CMM components are typically designed to be as stiff as possible which often results in large, heavy machines.
Significant improvements in CMM accuracy can be achieved if the positioning errors of the machine are pre-measured and compensation software is used to process the output data. This approach is currently in widespread use by CMM manufactures and allows the accuracy of the machines to be improved at a reasonable cost.
Despite the significant improvements in CMM performance over the past decade, several factors still limit CMM accuracy, speed and economic utility. Thermal variations in the CMM environment cause expansion and contraction of the individual components. This, in turn, distorts the elements of the kinematic structure, causing positioning errors of the probe tip. CMM manufacturers routinely supply algorithms to compensate for thermal expansion and contraction of the machine scales. Special software uses temperature sensors on the individual scales to modify the scale output based on the coefficient of thermal expansion of the scale material. If all parts of the machine are at the same temperature, then this approach is satisfactory. However, in an environment where the temperatures change or there are heat sources in the vicinity of the CMM, thermal gradients will occur in the machine structure. These gradients will distort the machine geometry in a manner which cannot be corrected by currently available methods, thus causing a serious degradation in the accuracy of the machine. For this reason, virtually all CMMs used for moderate- to high-precision inspection are housed in specially constructed rooms with carefully controlled environments. This requirement substantially increases the cost of CMM installation and usage. Furthermore, it forces the CMMs to be somewhat remote from the manufacturing floor, causing a disruption in the production flow and decreasing the utility of the machines.
A second limitation on CMMs performance is related to their dynamic performance. When large numbers of parts are being inspected, the inspection time becomes critical. For any given part geometry and features to be inspected, the inspection time is largely determined by the speed with which the CMM can move the probe tip from point to point. However, high speeds and accelerations are difficult to obtain when the kinematic structure is made up of large elements with significant mass. Furthermore, these machines typically possess very small damping, due in large part to the air-bearing slides used to reduce friction and hysteresis in the axis motions. The result is that significant vibrational deflections of the machine structure may occur when the machine speeds and accelerations are high. These deflections also cause a loss of accuracy and repeatability of the machines.
The CMM kinematic structure of the present invention is based on arranging the actuators in a parallel, as opposed to a serial, fashion. The most well-known example of a parallel manipulator is the Stewart Platform. Recently, machine tools based on variations of this architecture have been introduced. Parallel mechanisms of this type have six prismatic actuators connecting the moving body (platform) to the fixed body (base). Each of these actuators is connected to each of the bodies by spherical joints. By proper control of the individual actuator lengths, the position and orientation of the platform can be controlled in all six spatial degrees of freedom.
For fixed geometries of the base and platform, it is possible to formulate analytical expressions which give the position end orientation of the platform with respect to the base in terms of the lengths of the six actuators and the coordinates of the centers of each of the spherical joints on the base and platform. These expressions take the form of high order polynomials (up to 40th order), each root of which corresponds to a possible position and orientation.
Parallel mechanisms of this type are generally thought to possess outstanding rigidity relative to their weight. However, the reachable work volume tends to be small compared to the overall size of the machine. The first machine tools based on this architecture are just now becoming commercially available. More research, study and experience will be needed to assess their success or failure.
The design of a machine to perform precision dimensional measurement requires several basic tasks to be completed. First, a length reference (metric) and a means of transferring or establishing that metric in the workspace of the machine must be established. Second, a reference coordinate system whose origin and geometry are known must be established. Third, the generation of repeatable motions of the probe relative to the workpiece in a manner such that these motions can be measured relative to the reference coordinate system using the metric must be enabled. Fourth, the characteristics of the probe must be known since it links the measuring machine to the part being measured. The accuracy of the machine will depend on the degree of success in accomplishing each of these tasks.
A number of design principles which experience has shown will lead to accomplishing these tasks in an optimal manner are as follows:
1. Isolation of the device, which means that the disturbing effects of environmental factors such as temperature, humidity, vibration, etc., on the accuracy of the instrument should be minimized. Design strategies include control of the environment, decoupling from the environment and design of the instrument so that its response to these disturbances is minimal. Current generation CMMs typically make use of the first strategy, i.e., control of the environment. PA1 2. Whenever one body is mounted on another, the connection between the two should be designed to provide the minimum level of constraint necessary. Over-constraint or redundant constraints will cause the bodies to distort in a manner which is difficult or impossible to predict. The principle of exact mechanical constraint is termed "kinematic mounting." PA1 3. The alignment principle, or Abbe principle, is also known as "the first principle of mechanical design and dimensional metrology." Satisfaction of the alignment principle requires that the measurement axis of the displacement measuring system be placed so that its line of action passes through the point whose displacement is to be measured, i.e., the probe tip. If this is not possible, i.e., there exists an offset between the point of interest and the measurement axis, then the angular motions of the carriage must be measured and the displacement of the point must be calculated based on their effect. It is difficult or impossible to design a Cartesian mechanism so that the displacement measuring devices on the individual axes satisfy the Abbe principle. PA1 4. If possible, the metrology system should be separate from the structural loop which carries the forces due to the weights and inertias of the moving elements of the machine so that deformations of the structural members under these load do not induce metrology errors. Because of the added expense, most current generation CMMs do not use a separate metrology frame. PA1 1. The guideways should be as straight as possible. This is necessary since it is impossible to satisfy the Abbe alignment principle for all three axes. Therefore, extremely straight guideways are needed to prevent the moving bodies from rotating and causing displacement errors. It has been postulated that, using conventional practice (i.e., manufacturable at a reasonable cost), straightnesses of 1 .mu.m/m are achievable. PA1 2. The machine elements should be very stiff. Creation of very straight guideways is not sufficient if they sag under the weight of the moving bodies which they must support. This leads inevitably to large, heavy structures; i.e., qualities which are detrimental to the dynamic capabilities of the machine. PA1 3. The guideways must be aligned very precisely. The guideways essentially form the reference coordinate system for displacement measurements in many machines. Therefore, if they are snot arranged to be perfectly orthogonal to each other, measurement errors will result. PA1 4. A reliable and accurate displacement measuring system is required for measuring displacements of the individual slides along the guideways. PA1 1. The spherical joints should produce perfect spherical notion. The actuators must rotate about fixed points on the base and platform. PA1 2. The absolute distance between the centers of corresponding spherical joints on the base and platform must be measured with a high degree of accuracy. This is in distinct contrast to serial mechanisms where only the displacement along each axis is needed. In general, displacement measuring devices will be used to measure the changes in length of the individual legs. Therefore, a system for determining the initial lengths must be developed since it will be impossible to bring the joint centers on the base and platform into coincidence to make the leg length equal zero, thus providing an absolute reference for the displacement measuring system. PA1 3. The geometry of the base and platform must be stable and known to high accuracy. Since the position of the probe is dependent on the coordinates of the joint centers on the base and platform, it follows that any deformations of these bodies will cause errors in that position. Therefore, the base and platform should be rigid and thermally stable. This is a difficult design requirement since the base is physically large for machines with usefully large work volumes. Therefore, the joint centers are physically separated by a significant effective length of material. Any temperature changes in that material may result in significant changes of the geometry and lead to large positioning errors. This requirement can be relaxed if it is possible to monitor the actual positions of the joint centers while the instrument is in use.
The design principles given above can be used to formulate a set of design requirements necessary to obtain accuracy in Cartesian CMMs with a serial kinematic structure, as follows:
It is interesting to compare the design requirements for accuracy in parallel kinematic structures with those for serial kinematic structures. In parallel structures, the position and orientation of the moving body are obtained from the solution of a set of geometric relationships. The inputs to these relationships are the geometry of the base and platform (i.e. , the coordinates of the centers of the spherical joints), and the absolute lengths (distances between joint centers) of the six actuators. Therefore, in order to achieve accuracy in a parallel mechanism, one needs to realize the following requirements:
The first two requirements are descriptions of the functional capabilities of the laser ball bar (LBB), described in U.S. Pat. No. 5,428,446 issued Jun. 27, 1995. The LBB is essentially an extensible prismatic strut with spherical joints on the ends. These spherical joints are formed by precision spheres riding in magnetic sockets. The magnetic sockets maintain three-point contact with the spheres in conformance with the principle of kinematic mounting. Spheres with form accuracies better than 5 .mu.in (125 nm) are readily and inexpensively obtainable. When combined with the magnetic sockets, the resulting joint produces spherical motion to within 2.5 .mu.in (62.5 nm).
A laser interferometer is used with the LBB to measure displacements or length changes of the LBB. The initialization fixture allows the output of the interferometer to be initialized to the absolute distance between the centers of the spherical joints. In fact, the trilateration procedure used by the LBB to measure the spatial coordinates of the tool can be viewed as a degenerate form of Stewart platform mechanism. If the platform of such a mechanism shrinks to a single point so that all of the joint centers on it become coincident, then a tetrahedron is formed. The LBB sequentially measures the lengths of the sides of this tetrahedron to obtain the spatial coordinates of the apex. Thus, the LBB naturally satisfies two of the design requirements for accurate parallel mechanisms.
Thus, a need exists for an improved coordinate measuring machine (CMM) that satisfies the requirements set forth above, but does not have the disadvantages of known CMMs. There is a further need for a platform-type device with high positional accuracy, which device uses the LBB as a building block for creating the device.